73.5.21 problem 6.7 (i)

Internal problem ID [15132]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (i)
Date solved : Tuesday, January 28, 2025 at 07:36:08 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=2 \sqrt {2 x +y-3}-2 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 19

dsolve(diff(y(x),x)=2*sqrt(2*x+y(x)-3)-2,y(x), singsol=all)
 

\[ x -\sqrt {2 x +y-3}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.696 (sec). Leaf size: 34

DSolve[D[y[x],x]==2*Sqrt[2*x+y[x]-3]-2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2+2 e^{c_1} (x+1)+4+e^{2 c_1} \\ y(x)\to x^2+4 \\ \end{align*}